CPM Homework Help : CCA2 Problem 2-39

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2-39.

Make predictions about how many times the graph of each equation below will touch the $x$ -axis. You may first want to rewrite some of the equations in a more useful form.

$y=(x−2)(x−3)$
Hint (a):
How many $x$ -intercepts are there?
Answer (a):
$2$

$y=(x+1)^2$
Answer (b):
$1$

$y=x^2+6x+9$
Answer (c):
$1$

$y=x^2+7x+10$
Hint (d):
Look at parts (a) through (c). Remember to factor first to find the $x$ -intercepts.

$y=x^2+6x+8$
Hint (e):
Look at parts (a) through (d).

$y=−x^2−4x−4$
Hint (f):
Look at parts (a) through (d). Remember to factor $-1$ out.

Check your predictions with your calculator.
Write a clear explanation describing how you can tell whether the graph of a parabola will touch the $x$ -axis at only one point.
Hint (h):
What pattern did you notice above?

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